English
Related papers

Related papers: Learning with a linear loss function. Excess risk …

200 papers

Conventional techniques for supervised classification constrain the classification rules considered and use surrogate losses for classification 0-1 loss. Favored families of classification rules are those that enjoy parametric…

Machine Learning · Statistics 2019-06-03 Santiago Mazuelas , Andrea Zanoni , Aritz Perez

We prove risk bounds for binary classification in high-dimensional settings when the sample size is allowed to be smaller than the dimensionality of the training set observations. In particular, we prove upper bounds for both 'compressive…

Statistics Theory · Mathematics 2017-09-29 Ata Kaban , Robert J. Durrant

In this work we investigate to which extent one can recover class probabilities within the empirical risk minimization (ERM) paradigm. The main aim of our paper is to extend existing results and emphasize the tight relations between…

Machine Learning · Computer Science 2020-07-22 Alexander Mey , Marco Loog

It has been observed that certain loss functions can render deep-learning pipelines robust against flaws in the data. In this paper, we support these empirical findings with statistical theory. We especially show that empirical-risk…

Machine Learning · Computer Science 2020-09-15 Johannes Lederer

The well-known empirical risk minimization (ERM) principle is the basis of many widely used machine learning algorithms, and plays an essential role in the classical PAC theory. A common description of a learning algorithm's performance is…

Machine Learning · Statistics 2025-01-31 Steve Hanneke , Mingyue Xu

Learning models that are robust to distribution shifts is a key concern in the context of their real-life applicability. Invariant Risk Minimization (IRM) is a popular framework that aims to learn robust models from multiple environments.…

Machine Learning · Computer Science 2023-04-04 Moulik Choraria , Ibtihal Ferwana , Ankur Mani , Lav R. Varshney

We present a novel notion of complexity that interpolates between and generalizes some classic existing complexity notions in learning theory: for estimators like empirical risk minimization (ERM) with arbitrary bounded losses, it is upper…

Machine Learning · Computer Science 2017-10-24 Peter D. Grünwald , Nishant A. Mehta

In risk-sensitive learning, one aims to find a hypothesis that minimizes a risk-averse (or risk-seeking) measure of loss, instead of the standard expected loss. In this paper, we propose to study the generalization properties of…

Machine Learning · Statistics 2021-01-05 Jaeho Lee , Sejun Park , Jinwoo Shin

In this work we consider the learning setting where, in addition to the training set, the learner receives a collection of auxiliary hypotheses originating from other tasks. We focus on a broad class of ERM-based linear algorithms that can…

Machine Learning · Computer Science 2016-10-19 Ilja Kuzborskij , Francesco Orabona

Empirical risk minimization (ERM) is ubiquitous in machine learning and underlies most supervised learning methods. While there has been a large body of work on algorithms for various ERM problems, the exact computational complexity of ERM…

Computational Complexity · Computer Science 2017-04-11 Arturs Backurs , Piotr Indyk , Ludwig Schmidt

Researchers have widely used exploratory factor analysis (EFA) to learn the latent structure underlying multivariate data. Rotation and regularised estimation are two classes of methods in EFA that they often use to find interpretable…

Methodology · Statistics 2023-02-01 Xinyi Liu , Gabriel Wallin , Yunxiao Chen , Irini Moustaki

We consider a general statistical learning problem where an unknown fraction of the training data is corrupted. We develop a robust learning method that only requires specifying an upper bound on the corrupted data fraction. The method…

Machine Learning · Statistics 2020-02-10 Muhammad Osama , Dave Zachariah , Peter Stoica

Supervised classification techniques use training samples to learn a classification rule with small expected 0-1 loss (error probability). Conventional methods enable tractable learning and provide out-of-sample generalization by using…

Machine Learning · Statistics 2023-08-21 Santiago Mazuelas , Mauricio Romero , Peter Grünwald

Principal component analysis (PCA) frequently suffers from the disturbance of outliers and thus a spectrum of robust extensions and variations of PCA have been developed. However, existing extensions of PCA treat all samples equally even…

Machine Learning · Computer Science 2021-03-23 Rui Zhang , Hongyuan Zhang , Xuelong Li

Many practical optimization problems lack strong convexity. Fortunately, recent studies have revealed that first-order algorithms also enjoy linear convergences under various weaker regularity conditions. While the relationship among…

Optimization and Control · Mathematics 2026-02-05 Feng-Yi Liao , Lijun Ding , Yang Zheng

Minimax problems have achieved success in machine learning such as adversarial training, robust optimization, reinforcement learning. For theoretical analysis, current optimal excess risk bounds, which are composed by generalization error…

Machine Learning · Computer Science 2024-10-14 Bowei Zhu , Shaojie Li , Yong Liu

We present an extension of Vapnik's classical empirical risk minimizer (ERM) where the empirical risk is replaced by a median-of-means (MOM) estimator, the new estimators are called MOM minimizers. While ERM is sensitive to corruption of…

Statistics Theory · Mathematics 2018-08-10 Guillaume Lecué , Matthieu Lerasle , Timothée Mathieu

Here we propose a general theoretical method for analyzing the risk bound in the presence of adversaries. Specifically, we try to fit the adversarial learning problem into the minimax framework. We first show that the original adversarial…

Machine Learning · Statistics 2019-01-25 Zhuozhuo Tu , Jingwei Zhang , Dacheng Tao

This paper considers batch Reinforcement Learning (RL) with general value function approximation. Our study investigates the minimal assumptions to reliably estimate/minimize Bellman error, and characterizes the generalization performance…

Machine Learning · Computer Science 2021-03-26 Yaqi Duan , Chi Jin , Zhiyuan Li

We give a general result concerning the rates of convergence of penalized empirical risk minimizers (PERM) in the regression model. Then, we consider the problem of agnostic learning of the regression, and give in this context an oracle…

Statistics Theory · Mathematics 2008-10-30 S. Gaïffas , G. Lecué